Finite-dimensional pointed Hopf algebras over finite 3 simple groups of Lie type V. Mixed classes in Chevalley 4 and Steinberg groups

Autores
Andruskiewitsch, Nicolas; Carnovale, Giovanna; García, Gastón Andrés
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We show that all classes that are neither semisimple nor unipotent in finite simple Chevalley or Steinberg groups different from PSLn(q) collapse (i.e. are never the support of a finite-dimensional Nichols algebra). As a consequence, we prove that the only finite-dimensional pointed Hopf algebra whose group of group-like elements is PSp2n(q) , PΩ4n+(q), PΩ4n-(q), 3D4(q) , E7(q) , E8(q) , F4(q) , or G2(q) with q even is the group algebra.
Fil: Andruskiewitsch, Nicolas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Carnovale, Giovanna. Università di Padova; Italia
Fil: García, Gastón Andrés. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
Materia
NICHOLS ALGEBRA
HOPF ALGEBRA
RACK
FINITE GROUP OF LIE TYPE
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/140840
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Finite-dimensional pointed Hopf algebras over finite 3 simple groups of Lie type V. Mixed classes in Chevalley 4 and Steinberg groupsAndruskiewitsch, NicolasCarnovale, GiovannaGarcía, Gastón AndrésNICHOLS ALGEBRAHOPF ALGEBRARACKFINITE GROUP OF LIE TYPEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We show that all classes that are neither semisimple nor unipotent in finite simple Chevalley or Steinberg groups different from PSLn(q) collapse (i.e. are never the support of a finite-dimensional Nichols algebra). As a consequence, we prove that the only finite-dimensional pointed Hopf algebra whose group of group-like elements is PSp2n(q) , PΩ4n+(q), PΩ4n-(q), 3D4(q) , E7(q) , E8(q) , F4(q) , or G2(q) with q even is the group algebra.Fil: Andruskiewitsch, Nicolas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Carnovale, Giovanna. Università di Padova; ItaliaFil: García, Gastón Andrés. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; ArgentinaSpringer2020-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/140840Andruskiewitsch, Nicolas; Carnovale, Giovanna; García, Gastón Andrés; Finite-dimensional pointed Hopf algebras over finite 3 simple groups of Lie type V. Mixed classes in Chevalley 4 and Steinberg groups; Springer; Manuscripta Mathematica; 23; 6-2020; 621-6550025-26111432-1785CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10468-019-09868-6info:eu-repo/semantics/altIdentifier/doi/10.1007/s00229-020-01248-5info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1812.11566info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:55:16Zoai:ri.conicet.gov.ar:11336/140840instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:55:17.223CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Finite-dimensional pointed Hopf algebras over finite 3 simple groups of Lie type V. Mixed classes in Chevalley 4 and Steinberg groups
title Finite-dimensional pointed Hopf algebras over finite 3 simple groups of Lie type V. Mixed classes in Chevalley 4 and Steinberg groups
spellingShingle Finite-dimensional pointed Hopf algebras over finite 3 simple groups of Lie type V. Mixed classes in Chevalley 4 and Steinberg groups
Andruskiewitsch, Nicolas
NICHOLS ALGEBRA
HOPF ALGEBRA
RACK
FINITE GROUP OF LIE TYPE
title_short Finite-dimensional pointed Hopf algebras over finite 3 simple groups of Lie type V. Mixed classes in Chevalley 4 and Steinberg groups
title_full Finite-dimensional pointed Hopf algebras over finite 3 simple groups of Lie type V. Mixed classes in Chevalley 4 and Steinberg groups
title_fullStr Finite-dimensional pointed Hopf algebras over finite 3 simple groups of Lie type V. Mixed classes in Chevalley 4 and Steinberg groups
title_full_unstemmed Finite-dimensional pointed Hopf algebras over finite 3 simple groups of Lie type V. Mixed classes in Chevalley 4 and Steinberg groups
title_sort Finite-dimensional pointed Hopf algebras over finite 3 simple groups of Lie type V. Mixed classes in Chevalley 4 and Steinberg groups
dc.creator.none.fl_str_mv Andruskiewitsch, Nicolas
Carnovale, Giovanna
García, Gastón Andrés
author Andruskiewitsch, Nicolas
author_facet Andruskiewitsch, Nicolas
Carnovale, Giovanna
García, Gastón Andrés
author_role author
author2 Carnovale, Giovanna
García, Gastón Andrés
author2_role author
author
dc.subject.none.fl_str_mv NICHOLS ALGEBRA
HOPF ALGEBRA
RACK
FINITE GROUP OF LIE TYPE
topic NICHOLS ALGEBRA
HOPF ALGEBRA
RACK
FINITE GROUP OF LIE TYPE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We show that all classes that are neither semisimple nor unipotent in finite simple Chevalley or Steinberg groups different from PSLn(q) collapse (i.e. are never the support of a finite-dimensional Nichols algebra). As a consequence, we prove that the only finite-dimensional pointed Hopf algebra whose group of group-like elements is PSp2n(q) , PΩ4n+(q), PΩ4n-(q), 3D4(q) , E7(q) , E8(q) , F4(q) , or G2(q) with q even is the group algebra.
Fil: Andruskiewitsch, Nicolas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Carnovale, Giovanna. Università di Padova; Italia
Fil: García, Gastón Andrés. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina
description We show that all classes that are neither semisimple nor unipotent in finite simple Chevalley or Steinberg groups different from PSLn(q) collapse (i.e. are never the support of a finite-dimensional Nichols algebra). As a consequence, we prove that the only finite-dimensional pointed Hopf algebra whose group of group-like elements is PSp2n(q) , PΩ4n+(q), PΩ4n-(q), 3D4(q) , E7(q) , E8(q) , F4(q) , or G2(q) with q even is the group algebra.
publishDate 2020
dc.date.none.fl_str_mv 2020-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/140840
Andruskiewitsch, Nicolas; Carnovale, Giovanna; García, Gastón Andrés; Finite-dimensional pointed Hopf algebras over finite 3 simple groups of Lie type V. Mixed classes in Chevalley 4 and Steinberg groups; Springer; Manuscripta Mathematica; 23; 6-2020; 621-655
0025-2611
1432-1785
CONICET Digital
CONICET
url http://hdl.handle.net/11336/140840
identifier_str_mv Andruskiewitsch, Nicolas; Carnovale, Giovanna; García, Gastón Andrés; Finite-dimensional pointed Hopf algebras over finite 3 simple groups of Lie type V. Mixed classes in Chevalley 4 and Steinberg groups; Springer; Manuscripta Mathematica; 23; 6-2020; 621-655
0025-2611
1432-1785
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10468-019-09868-6
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00229-020-01248-5
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1812.11566
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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